Question

The following data contains the characteristics of 30 motorcycles that will be analyzed using a Regression model. You will study the relationship between a motorcycles' engine power (measured in horsepower) and the motorcycles' weight (measured in pounds).

Power (cf): 145 215 165 85 225 87 175 210 158 86 150 150 76 170 208 150 215 225 220 153 175 130 140 165 180 150 190 110 150 86

Weight (lb): 4082 4735 3693 2310 4951 2672 4464 4382 4363 2220 4135 4096 2065 4654 4633 4464 4615 4425 4354 4129 5140 3504 3449 4209 4955 4997 3850 2962 3761 2226

Declare:

a) Explanatory variable:

b) Response variable:

c) Make a scatter diagram. Describe the axes and scales for each axis.

d) What can you say about the strength, direction, and shape? Answer this subjectively (do not calculate the correlation).

e) Assuming that the scatter diagram above is linear with r2 = 0.7142182. Determine the slope and intercept of the regression line. (use the r program to calculate Sweight, Spower.

f) Write the modeled regression line.

g) Interpret the slope

h) What would be the engine power of a car if its weight were 2.5 tons? h.

i) Plot the regression line on the scatter plot

j) Interpret r. agrees with what was thought in point c

k) Interpret r2

Answer 1

a) Explanatory variable: Weight

b) Response variable:Power

c) The scatter diagram

d) tthe strength is strong ,direction is positive , shape is linear .

e)

Simple Linear Regression Analysis
Regression Statistics
Multiple R	0.8451
R Square	0.7142
Adjusted R Square	0.7040
Standard Error	24.3807
Observations	30
ANOVA
	df	SS	MS	F	Significance F
Regression	1	41595.6860	41595.6860	69.9768	0.0000
Residual	28	16643.7806	594.4207
Total	29	58239.4667
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-8.5030	20.4114	-0.4166	0.6802	-50.3139	33.3079
Weight	0.0422	0.0050	8.3652	0.0000	0.0319	0.0525

the slope and intercept of the regression line is 0.422 and -8.5030 respectively   

f) the modeled regression line. is y = -8.5030 + 0.0422 x

g) For every 1lb increase in weight the power of vehicle increase by 0.0422cf

h) the engine power of a car if its weight were 2.5 tons would be -8.5030 + 0.0422*5511.56 = 224.08

i) Plot the regression line on the scatter plot

j) r. = 08451 , there is positive strong linear correlation between power and weight . yes it agrees with what was thought in point c

k) r2= 07142 , about 7142% variation in power can be explained by this model